Special Relativity (i'm confused)

[SinghRP]

Answer to the first question:
The speed of light (electromagnetic wave or photon) is the same c = 3.0x10**8 m/s regardless of the observer's frme. That is, c+c = c.
This is one of the special relativity's two postulates.

 

[ghwellsjr]

Answer to the first question:
The speed of light (electromagnetic wave or photon) is the same c = 3.0x10**8 m/s regardless of the observer's frme. That is, c+c = c.
This is one of the special relativity's two postulates.

I'm not sure what the first question was but here are the facts:

Anyone who measures the round-trip speed of light will get c. This has nothing to do with relativity. It was an experimentally derived observation that any theory of light, time, space, etc must take into account and has nothing to do with frames of reference, except that the measurement must be made while the experimental apparatus is not accelerating so it is sometimes noted that the experiment must be performed in an inertial frame. The measurement has been performed so many times and to such accuracy that we now assign an exact value to c.

The one-way speed of light is a postulate of Special Relativity and cannot be measured. This does have to do with frames of reference but has nothing to do with any observer. When you are composing and describing a situation, you can pick any frame of reference and if you want you can put any number of observers, objects, light sources, reflectors, etc at any speeds within that frame, doing anything you want them to be doing. Then you can analyze the situation in that frame. Then if you want, and if you really understand SR, you can transform the entire situation into a new frame of reference that itself is described as having a speed and direction relative to the first frame.

So, if we take the original scenario the way newbiephysics described it, it was:

A light source (he implied some sort of a flash) stationary in the frame and one light year away are two observers, one that remains stationary in the frame, and the other one accelerates to some speed in some undefined way (but it won't make any significant difference) toward the flash of light. If you analyze this situation as it was given, you can say that it will take one year for the flash of light to travel from its source to the stationary observer and less time for the flash to reach the moving observer, simply because the moving observer is now between the source of the light and the stationary observer.

In a previous post (#11), I have already described how each observer can measure the round-trip speed of light as it passes by them (and is reflected off a mirror some known distance away from them--it takes two different mirrors, one for each observer) and they will both measure c. It is only for the stationary observer in the frame that is used to describe the situation that we can say that the one-way speed of light is c. If you want to transform the situation into a different frame, say the one in which the moving observer has attained his final constant speed, then you have to be very astute at SR. JesseM has described how to do this and how important it is to do it correctly. If you leave something out, you will get the wrong answer.

And one of the frames that you cannot transform the situation into is the so-called frame of the flash of light. Light does not have a frame and if you try to do it, you will get nonsense. Later, I will try to address Grimble's concerns, but it is going to be tough, because it is based on an illegal analysis.

 

[ghwellsjr]

...
I was agreeing with Jesse that they are only relevant when using different frames of reference, whereas I am only using the light's frame of reference.

Grimble, I was going to try to go through your answers in detail but there is no point because you are trying to analyze the situation in "the light's frame of reference". One reason that I have been saying that light doesn't have a frame of reference is because when we talk about an observer or an object or anything having a frame a reference or being in a frame of reference, we mean the frame in which that thing is at rest. SR states that the one-way speed of light is c in any frame of reference. Light cannot both be at rest and be traveling at c at the same time in the same frame. It's pointless to even think about what would be happening in such as situation. It's like dividing zero by zero, you can get any answer you want.

But what you can do is analyze the trajectory of the flash of light as it travels from its source to the stationary observer, one light year away, in the frame in which both the source and the observer are stationary: The flash occurs at the same instant that the moving observer leaves the stationary observer. The flash is traveling at c in the frame towards both observers while the moving observer is traveling toward the flash (and its source) at some unspecified speed. Eventually, the flash reaches the moving observer somewhere between the source of light and the stationary observer. At this point, the moving observer sees the flash and it continues on its way behind him. Later (in fact, one year after the flash left its source), the flash reaches the stationary observer and he sees the flash. This is the analysis that shows that the flash first encounters the moving observer and then the stationary observer. There is nothing wrong with this analysis and it is the simplest one to do. If you want to analyze the same situation in a different frame, you better get the same answer or you have done something wrong.

Does this clear up the situation for you or do you still want to try to defend the position that the flash of light reaches both observers at the same time?

 

[ghwellsjr]

I think there is a sense in which ghwellsjr right that 'this should seem obvious' without taking account of simultaneity, or length contraction. I don't know how this relates the OP's way of looking at it. This 'obvious' way of looking at it wrong in all the details, but a newbie might see nothing wrong with it.

What am I talking about? Assume stationary observer (SO), supernova (SN) a light year away at rest relative to SO, and moving observer (MO) who passes SO simultaneously with the SN event (as perceived by SO). Suppose MO moving at 2/3 c. MO moves .4 light years in .6 years , seeing the SN at that point. They see the light earlier; they see the light coming to them as having traveled .6 light years in .6 years, thus speed c. Later (.4 year later), SO sees the SN, and computes that speed was also c. At first glance, no contradiction or issue.

In fact, this is even 'correct' all the way through if MO chose to do all measurements and analysis from SO frame. You can even make it seem to work in MO frame. SN is moving toward MO at 2/3 c. If SN event occurred 1 light year from MO passing SO, and light is same speed in all frames, then MO now thinks light should take a year to reach them, having traveled a light year. Still ok, time different in MO frame, but c comes out same. SN signal will take 3 years to reach SO, having traveled 3 light years. So with this simplistic analysis, both observers see light moving at c, both think MO sees SN first, the only difference is time: SO thinks the two times are .6 years and 1 year, while MO thinks they are 1 year and 3 years.

So I can see a newbie wondering arriving at the idea you need time dilation (in the wrong amount), but what's this about simultaneity and length contraction?

Anyway, I think it could be worthwhile explaining in detail what is wrong with this picture. I don't have time to do it right now.

I can see lots of things wrong with this picture. Were you attempting to illustrate another way that newbiephysics could have gotten confused on this situation? Are you ever going to have time to explain what is wrong? I can't tell what you were trying to do in this post.

 

[Grimble]

Grimble, I was going to try to go through your answers in detail but there is no point because you are trying to analyze the situation in "the light's frame of reference". One reason that I have been saying that light doesn't have a frame of reference is because when we talk about an observer or an object or anything having a frame a reference or being in a frame of reference, we mean the frame in which that thing is at rest. SR states that the one-way speed of light is c in any frame of reference. Light cannot both be at rest and be traveling at c at the same time in the same frame. It's pointless to even think about what would be happening in such as situation. It's like dividing zero by zero, you can get any answer you want.

But what you can do is analyze the trajectory of the flash of light as it travels from its source to the stationary observer, one light year away, in the frame in which both the source and the observer are stationary: The flash occurs at the same instant that the moving observer leaves the stationary observer. The flash is traveling at c in the frame towards both observers while the moving observer is traveling toward the flash (and its source) at some unspecified speed. Eventually, the flash reaches the moving observer somewhere between the source of light and the stationary observer. At this point, the moving observer sees the flash and it continues on its way behind him. Later (in fact, one year after the flash left its source), the flash reaches the stationary observer and he sees the flash. This is the analysis that shows that the flash first encounters the moving observer and then the stationary observer. There is nothing wrong with this analysis and it is the simplest one to do. If you want to analyze the same situation in a different frame, you better get the same answer or you have done something wrong.

Does this clear up the situation for you or do you still want to try to defend the position that the flash of light reaches both observers at the same time?

Yes and thank you for your patience and time, ghwellsjr. That makes perfect sense.

Would it be correct then, to consider that the light moves between two points in space and time (events?) without any consideration of the movement of source and/or destination: i.e. regardless of the frame of reference from which it is observed?

(I know, maybe I am being silly but I'm trying to comprehend the speed of light being the same in any frame of reference, but please bear with me)

And as the speed of light is a physical limit and the 'dilated time' from another FoR is always zero, the speed of the observers frame is irrelevant as 'relative' path of the light is instant.

If you can follow my thoughts here?

 

[ghwellsjr]

Yes and thank you for your patience and time, ghwellsjr. That makes perfect sense.

Would it be correct then, to consider that the light moves between two points in space and time (events?) without any consideration of the movement of source and/or destination: i.e. regardless of the frame of reference from which it is observed?

Yes, as long as you realize that a frame of reference is not a physical thing. It is an arbitrary assignment that we humans apply to a situation in which to describe and analyze the entire situation. You must maintain that one frame of reference throughout your analysis. Think of it as a co-ordinate system.

(I know, maybe I am being silly but I'm trying to comprehend the speed of light being the same in any frame of reference, but please bear with me)

Any one who measures the round-trip speed of light, will get the same answer, c, no matter what their speed is relative to any frame of reference or relative to anyone else. In fact, you don't need to consider a frame of reference when you perform this physical experiment, as long as the person doing the measurement is traveling at a constant speed and not accelerating. But it is in only one frame of reference at a time that the one-way speed of light is assigned to be c. The one-way speed of light cannot be measured. When you say that it is c, you are defining a frame of reference.

And as the speed of light is a physical limit and the 'dilated time' from another FoR is always zero, the speed of the observers frame is irrelevant as 'relative' path of the light is instant.

If you can follow my thoughts here?

This thought, I cannot follow. The run-trip speed of light is always physically measured to be the constant c. I don't know why you would say "the 'dilated time' from another FoR is always zero". You could say that in your assigned FoR, the dilated time for a very fast moving object approaches zero but this is speed dependent. The faster the object goes, the slower time goes for that object but it can never reach zero. And it isn't "from another FoR". The rest of your comment also doesn't make any sense.

 

[PAllen]

I can see lots of things wrong with this picture. Were you attempting to illustrate another way that newbiephysics could have gotten confused on this situation? Are you ever going to have time to explain what is wrong? I can't tell what you were trying to do in this post.

Yes, I was trying to give an example of how someone could produce a confused analysis that seems plausible to a newbie. Sorry, but I don't think I will get back to writing up the mistakes. I would be more motivated if someone had asked about this 'analysis', but since it was a strawman scenario anyway, I don't feel inclined to write up a critique. If you want to, go ahead, but it seems it doesn't really have much to do with newbiephysics misunderstangs.

 

[PAllen]

Yes, I was trying to give an example of how someone could produce a confused analysis that seems plausible to a newbie. Sorry, but I don't think I will get back to writing up the mistakes. I would be more motivated if someone had asked about this 'analysis', but since it was a strawman scenario anyway, I don't feel inclined to write up a critique. If you want to, go ahead, but it seems it doesn't really have much to do with newbiephysics misunderstangs.

Ok, I will at least point out one of the first and largest mistakes of my strawman scenario. I propose that both the stationary observer (relative to the star) and the moving observer, both perceive the star as 1 light year away at the time the moving observer passes the stationary observer. This is trivially impossible. Pick any method of measuring distance that you want, and it can't be true that they both measure it as 1 light year at this point. Everything following this is then invalid.

 

[yuiop]

Would it be correct then, to consider that the light moves between two points in space and time (events?) without any consideration of the movement of source and/or destination: i.e. regardless of the frame of reference from which it is observed?

Yes, this is correct (and important).

(I know, maybe I am being silly but I'm trying to comprehend the speed of light being the same in any frame of reference, but please bear with me)

The most intuitive way to understand how this comes about is to use Lorentz Ether theory which assumes the speed of light is always constant relative to some assumed Lorentz ether background. Clocks and rulers moving relative to this background time dilate and length contract respectively in such a way that any observer using his co-moving clocks and rulers will measure the speed of light to be the same as any other observer regardless of the their motion relative to the background. Lorentz Ether Theory is correct and accurate in predictions which agree with SR but is unfashionable these days because it is impossible to determine which observer is "really" at rest with this background and any observer can be arbitrarily chosen to be at rest with this background and the results come out the same. Einstein concluded "we have no need of it" and dispensed with the Lorentz ether, but in some ways it more intuitive.

The constancy of the speed of light in SR can be demonstrated using the relativistic velocity addition formula:

$$Vca = \frac{Vcb + Vba}{1+Vcb*Vba}$$

where:
Vcb is the velocity of c according to observer b.
Vba is the velocity of b according to observer a.
Vca is the velocity of c according to observer a.

If we say Vcb is the velocity of a photon according to b and set it equal to 1, and the velocity Vba of b according to a is 0.7 then the velocity of the photon Vca according to a is:

$$Vca = \frac{1 + 0.7}{1+1*0.7} = 1$$

so it is easy to see that whatever the speed of b relative to a, if observer b sees the speed of light to be 1 then observer a must also see the speed of light to be 1.

Of course the relativistic velocity addition equation is formulated using the postulates of SR that assume the speed of light is constant for all observers so it does not really explain "why" the speed of light behaves that way.

 

[PAllen]

I thought of a nice argument that you can conclude that the moving observer (as described in the original post) must receive the light from the distant object first, without caring about SR vs Galilean physics. Suppose the moving observer is a polarizing filter. It is obvious that the stationary observer sees the moving observer receive light from the distant source first. This means that the stationary observer receives polarized light. Unless one posits SR declares that it is observer dependent whether polarized vs. non-polarized light interacts with an object, you must conclude that this will be true for all observers.

 

[Passionflower]

Do I get this right?

Consider seven friends at coordinate time t₀ at the same position in space. The are considering an object a coordinate distance of 10 away. Each has a different velocity or acceleration.

Friend1: v=0
Friend2: v=0.9
Friend3: v=0.8
Friend4: v=0.6
Friend5: v=0, a=0.1
Friend6: v=0, a=0.3
Friend7: v=0, a=1

How do they view distance in time?

For friend 1 to 4 we use:

$$d\sqrt {1-{v}^{2}}-tv$$

For friends 5, 6 and 7 we use:

$$d-{\frac {\cosh \left( at \right) -1}{a}}$$

Edit: updated information.

 

[yuiop]

Do I get this right?

Consider seven friends at coordinate time t₀ at the same position in space. The ate considering an object a coordinate distance of 10 away. Each has a different velocity or acceleration.

Friend1: v=0
Friend2: v=0.9
Friend3: v=0.8
Friend4: v=-0.9
Friend5: v=-0.8
Friend6: v=0, a=1
Friend7: v=0, a=-1

How do they view distance in time?

For friend 1 to 5 we use:

$$\gamma (d-tv)$$

Something isn't right. If you are plotting the distances as seen by the moving observers, then the initial coordinate at t=0 of observer 3 with v=0.8 should be x' = gamma(d-tv) = 1.666(10-0) = 16.666 and not 6.

The final coordinate of observer 3 when x'=0 seems to be correct at t=12.5 seconds.

If you are plotting the distances as seen by the observer that remains at distance 10 from the target, then the worldline of the observer moving with v=0.8 should have a slope of 0.8 which it does not.

 

[Passionflower]

Something isn't right. If you are plotting the distances as seen by the moving observers, then the initial coordinate at t=0 of observer 3 with v=0.8 should be x' = gamma(d-tv) = 1.666(10-0) = 16.666 and not 6.

You are right, the formula should be:

$$d\sqrt {1-{v}^{2}}-tv$$

Thanks for pointing that out, I updated the data accordingly.

If you are plotting the distances as seen by the observer that remains at distance 10 from the target, then the worldline of the observer moving with v=0.8 should have a slope of 0.8 which it does not.

This graph is comparing the distances from the perspective of different observers, it is not a traditional spacetime diagram.

Here is a plot:
[PLAIN]http://img268.imageshack.us/img268/1189/lossieteamigos2.gif

As you can see the blue, orange and green friends all start at a different observed distance at t=0, while the three accelerating ones start at the same as the stationary one since the Lorentz factor at t=0 is 1 for the accelerating friends. Of course we could start accelerating from a given velocity as well.

Here is a general plot:
[PLAIN]http://img9.imageshack.us/img9/2584/velocityandacceleration.gif
The maximum acceleration plotted was 1 which is an arbitrary maximum I imposed on the plot.

It would be nice if we could do a similar one with the Doppler factor for those velocities and accelerations, anyone want's to take a stab at that one? Especially the accelerating ones would be interesting.

 

[Grimble]

Ok, I will at least point out one of the first and largest mistakes of my strawman scenario. I propose that both the stationary observer (relative to the star) and the moving observer, both perceive the star as 1 light year away at the time the moving observer passes the stationary observer. This is trivially impossible. Pick any method of measuring distance that you want, and it can't be true that they both measure it as 1 light year at this point. Everything following this is then invalid.

I'm sorry but surely if you reworded that slightly and said "... moving observer, [STRIKE]both[/STRIKE]/each perceive the star as 1 light year away ..." Then it would not be impossible but what would actually be what had to be...

Each observer, at rest, in his own frame of reference, measuring with his own 'rulers' and 'clocks' stationary in his reference frame, would measure the distance to the star as 1 Proper light year, would they not.

I.e. Each could have a clock at rest with themselves and each could theoretically have a clock, at rest in their frame, adjacent to the star at the moment they pass.

So what I feel that you are saying is that they couldn't Both be one light year away in the same frame of reference.

Yet is that true? For if one, say the stationary one measured the distance of the moving one from the star as they passed, using his own 'rulers' and 'clocks' then he would surely arrive at the same measure for both.

It is only when he uses his own 'rulers and 'clocks' to measure his distance and the moving observer's 'rulers' and 'clocks' to measure the mover's distance that the distances have to be different due to the Lorentz transformations.

 

[ghwellsjr]

You have to make a distinction between what is defined to be true in the scenario and what "observers" in the scenario would perceive. The definition of this scenario is that the two observers are one light year away from the light source at the moment the flash occurred. But neither one of them can perceive the flash or have any knowledge of this fact until some time later when the flash of light progresses to wherever they happen to be.

Remember, PAllen was attempting to describe how a naive person could misunderstand the scenario and conclude that the flash of light reached both observers at the same time. So it is very difficult for me to know if you are attempting to do the same thing, describe an incorrect understanding of the situation or if you are trying to be an astute person and describe a correct understanding of the scenario.

I'm not interested in discussing how a naive person can get confused, I'm interested in removing the confusion and discussing a correct analysis. The easiest correct analysis is to use the same frame of reference in which the scenario was stated to describe what happens. If you want to transform this particular scenario into another frame of reference (rather than define a new scenario from the point of view of another frame of reference) then you must be very astute to make that transformation. This is what JesseM was describing in his first post, you have to take into account all the aspects of SR and you have to know what your are doing, if you leave something out, you will be describing a different scenario and you can get a different answer.